Telescope based calibration of a three dimensional optical scanner

ABSTRACT

An embodiment of the invention includes using a set of telescopes to calibrate a three dimensional optical scanner. Three separate calibrations are disclosed for a survey grade calibration: (1) angular calibration, implemented using at least one anti-podal pair of telescopes, (2) range calibration, implemented using at least one telescope mounted fiber recirculator, and (3) tilt calibration, implemented using at least one pair of telescopes not mounted in anti-podal configuration and an integral tilt table. Methods for aligning or measuring the mis-alignment between anti-podal telescope pairs are also described.

CROSS-REFERENCE TO RELATED APPLICATIONS

Not applicable.

BACKGROUND OF THE INVENTION

The acquisition of data and subsequent generation of computer models forreal-world objects is of interest in many industries and for manyapplications including architecture, physical plant design,entertainment applications (e.g., in movies and games), surveying,manufacturing quality control, medical imaging and construction, as wellas cartography and geography applications. In order to obtain accurate3D models of an object, as well as the area in which that object existsin the real world, it is necessary to take accurate measurements, orsamplings of surfaces that make up the object, and elements of thesurrounding area. Historically, this sampling was carried out usingtechniques that provided samples at the rate of tens or hundreds perhour at most.

Recent advances in scanning technology, such as technologies utilizingLIDAR scanning, have resulted in the ability to collect billions ofpoint samples on physical surfaces, over large areas, in a matter ofhours. In a LIDAR scanning process, the scanning device scans a laserbeam across a scene that encompasses the structure of interest and thebeam reflected from the scene is captured by the scanning device. Thescanning device thus measures a large number of points that lie onsurfaces visible in the scene. Each scan point has a measured locationin 3D space, within some measurement error, that typically is recordedrelative to a point (x,y,z) in the local coordinate system of thescanner. The resulting collection of points is typically referred to asone or more point clouds, where each point cloud can include points thatlie on many different surfaces in the scanned view.

Conventional LIDAR scanning systems do not natively create points butinstead create sets of ranges with associated mirror angles which areconverted to x, y and z coordinates. The function which maps thesenative measurements into x, y and z coordinates depends on how thescanner was assembled and, for high accuracy systems, is different foreach scanner and is a function of temperature and other environmentalconditions. The differences between scanner systems are typicallyrepresented by a collection of numbers called calibration parameters.The purpose of a calibration system is to estimate the calibrationparameters.

Calibration systems for scanners today typically involve measuring acollection of known targets and from these observations estimating thecalibration parameters. The scanner system will measure the locations ofone or more targets. These same targets locations are measured by atrusted reference system, for example, a total station calibrated usingsome other method. The calibration parameters at this measurementcondition are then estimated. The aforementioned process might becarried out at one or more temperatures.

Such an approach suffers from at least three problems. First, asecondary measuring system is needed to locate the laser scannertargets. Second, if the targets move between the time the targets aremeasured with the secondary measuring system and when the targets aremeasured by the scanner being calibrated, perhaps because the targetsare, for example, affixed to portions of a building which deform withsunlight or other factors over time, these motions will introducesystematic errors into the calibration parameters. Third, the ability toestimate the calibration parameters is no better than the ability tolocate the targets with the scanner and the secondary measuring system.The further away a target is from the scanner the better the estimate ofthe angle portion of the calibration becomes. This has led the state ofthe art to large calibration systems with widely spaced targets. Thisrequires a large stable space. The size of the space is costly and tendsto aggravate the second problem; that is, targets remaining stable orfixed in position over time.

A total station is a manually operated optical instrument used insurveying. A total stations is a combination of an electronic theodolite(transit), an electronic distance meter (EDM) and software running on anexternal computer known as a data collector. With a total station onemay determine angles and distances from the instrument to points to besurveyed. With the aid of trigonometry and triangulation, the angles anddistances may be used to calculate the coordinates of actual positions(x, y, and z or northing, easting and elevation) of surveyed points, orthe position of the instrument from known points, in absolute terms.Most modern total station instruments measure angles by means ofelectro-optical scanning of extremely precise digital bar-codes etchedon rotating glass cylinders or discs within the instrument. The bestquality total stations are capable of measuring angles down to 0.5arcseconds. Inexpensive “construction grade” total stations cangenerally measure angles to 5 or 10 arcseconds.

Total stations solve the high accuracy angular calibration problem byusing collimating telescopes. The total station to be calibrated isplaced on a stable fixture. Telescopes, which have a target behind a setof lenses, are used as targets. By placing a set of lenses in front oftheir targets, the target appears to be located at a great distance,perhaps even hundreds of meters away when in fact the target is lessthan one meter away. This technique reduces the size of the angularportion of the total station calibration system to a few square meters.The reduced size also helps with the stability of the targets, since thetargets are physically close together and can be mounted in the samestable base, typically made from concrete. Even the stability of thetargets is not critical. The total station calibration system removesthe need for a secondary measurement system or great stability byobserving these targets in both faces.

In a two face measurement the total station is placed onto a stablemount. The operator then observes the targets in the telescopes throughthe telescope of the total station. The measurement is repeated in thesecond face; that is, by rotating the total station by 180 degrees, orone half of a revolution, on its base and repeating the measurements.The angular measurements are saved and from these observations both thelocations of the telescopes and the relevant total station parameterscan be determined without the use of a secondary measurement system.

The collimating telescope needs some adaptation to be used for laserscanners because laser scanners emit a laser beam whose location needsto be found. Additionally, the total station calibration method of usingtwo face measurements and no secondary measurement system fails whenapplied to laser scanners. A typical laser scanner must move the laserbeam very quickly. Generally this is done by using mirrors instead of bymoving the laser. If the laser is moved entirely, the total stationmethod of calibration is applicable because the uncertainty in themounting of the laser beam behaves the same as the uncertainty in theelevation index and the total station collimation error. However, ifmirrors move the laser beam, the uncertainty in the laser mounting arenew parameters and the total station calibration method becomes illconditioned for laser scanner calibration.

In summary, the state of the art in scanner calibration suffers fromsize, cost, and accuracy limitations because the calibration needs asecondary reference and accuracy is sensitive to the size and stabilityof the calibration system. The state of the art in total stationcalibration solves these problems but fails when adapted to laserscanner calibration. The total station calibration method fails tocorrectly identify all calibration parameters of the laser scannerbecause the way such laser scanners are physically arranged is differentfrom total stations, i.e. because laser scanners use mirrors to deflectthe laser beam.

BRIEF SUMMARY OF THE INVENTION

This Summary is provided to introduce a selection of concepts in asimplified form that are further described below in the DetailedDescription. This Summary is not intended to identify key features oressential characteristics of the claimed subject matter, nor is itintended to be used as an aid in determining the scope of the claimedsubject matter.

An embodiment of the invention includes an antipodal calibration rig forperforming angular calibrations or tilt calibrations of threedimensional optical scanning systems. The antipodal calibration rigincludes a first telescope mounted on the rig and a second telescopemounted on the rig. The antipodal calibration rig also includes a basefor a scanner located within the antipodal calibration rig. The base isconfigured such that when the scanner is placed on the base the scanneris on an axis of the first telescope and an axis of the secondtelescope.

Another embodiment of the invention includes a method for aligning afirst telescope and a second telescope in an antipodal pair. Thetelescopes include alignment lasers and a means for observing the firsttelescope and second telescope is located between the first telescopeand second telescope. The method includes comparing the position of afirst beam of a first alignment laser of the first telescope against theposition of a second beam of a second alignment laser of the secondtelescope at the first telescope. The method also includes comparing theposition of the first beam against the position of the second beam atthe second telescope. The method further includes adjusting the firsttelescope and the second telescope until the beams of the firstalignment laser and second alignment laser are parallel.

Another embodiment of the invention includes a method for angularcalibration of a three dimensional optical scanning system. The methodincludes locating the three dimensional optical scanning system withinan antipodal calibration rig. The antipodal calibration rig includes afirst telescope mounted on the antipodal calibration rig and a secondtelescope mounted on the antipodal calibration rig. The first telescopeis aligned antipodal to the second telescope and the scanner is on anaxis of the first telescope and an axis of the second telescope. Themethod also includes measuring the angular location of the firsttelescope and measuring the angular location of the second telescope intwo faces. The method further includes estimating a set of angularcalibration parameters for the three dimensional optical scanning systemfrom the measurements.

Another embodiment of the invention includes a method for calibrating atilt sensor of a three dimensional optical scanning system. The methodincludes locating the scanning system on a tilt table within anantipodal calibration rig. The antipodal calibration rig includes one ormore telescopes mounted on the antipodal calibration rig. The one ormore telescopes are used to measure the tilt of the three dimensionaloptical scanning system. The method also includes performing an angularcalibration on the three dimensional optical scanning system and solvingfor a tilt index of the three dimensional optical scanning system.Solving for the tilt index involves rotating the scanner and observingthe changes of the tilt sensor and is well known in surveying as a twoface adjustment of the tilt. The method further includes performing aset of steps including: moving the tilt table to a next tilt position;obtaining an actual output of the tilt sensor; measuring the position ofthe two or more telescopes; and computing the expected output of thetilt sensor using the measured position of the two or more telescopes.The method includes repeating the set of steps for three or more tiltpositions of the three dimensional optical scanning system and computingan estimated tilt sensor model using the measurements.

Another embodiment of the invention includes a method for determining arange scale of a three dimensional optical scanning system. The methodincludes transmitting a beam from the three dimensional optical scanningsystem to a range calibration rig. The method also includes splittingthe beam from the three dimensional scanning system at the rangecalibration rig. The first portion of the beam from the threedimensional scanning system enters a recirculating fiber loop to bereturned to the beam splitter and the second portion from the threedimensional scanning system enters a transmitting lens. The methodfurther includes transmitting the beam from the transmitting lens backto the scanning system, measuring the time between pulses at thescanning system and calculating range data from the time between pulses.Two such assemblies can be placed on opposite sides of the scanner inorder to estimate the range offset of the scanning system.

These and other objects and features of the present invention willbecome more fully apparent from the following description and appendedclaims, or may be learned by the practice of the invention as set forthhereinafter.

BRIEF DESCRIPTION OF THE DRAWINGS

To further clarify the above and other advantages and features of thepresent invention, a more particular description of the invention willbe rendered by reference to specific embodiments thereof which areillustrated in the appended drawings. It is appreciated that thesedrawings depict only illustrated embodiments of the invention and aretherefore not to be considered limiting of its scope. The invention willbe described and explained with additional specificity and detailthrough the use of the accompanying drawings in which:

FIG. 1A illustrates an example of an antipodal calibration rig;

FIG. 1B illustrates a four axis scanner manipulator of FIG. 1A;

FIG. 2 is a flow diagram illustrating an example of a method foraligning a first telescope and a second telescope in an antipodal pair;

FIG. 3 illustrates an embodiment for comparing the position of alignmentlasers using a beam splitter;

FIG. 4 illustrates an alternative embodiment for comparing the positionof alignment lasers using corner cubes;

FIG. 5A illustrates a simulation of the error in calibration parametersdue to measurement noise;

FIG. 5B illustrates a simulation of the error in calibration parametersdue to misalignment of an antipodal pair of telescopes used incalibrating the scanner;

FIG. 6 is a flow diagram illustrating an example of a method forperforming an angular calibration of a three dimensional scanningsystem;

FIG. 7 is a flow diagram illustrating an example of a method forperforming a tilt calibration of a three dimensional scanning system;

FIG. 8 is a flow diagram illustrating an example of a method forperforming a range calibration of a three dimensional scanning system;

FIG. 9A illustrates an example of a range calibration rig; and

FIG. 9B illustrates the pulses transmitted from the range calibrationrig to the scanner.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Calibration of total stations, and other scanning systems, is a wellknown process. However, this process is not well suited to threedimensional optical scanning systems including LIDAR scanners. Threedimensional optical scanning systems have additional degrees ofuncertainty in their calibrations compared to total stations. Theseadditional degrees of uncertainty result from, among other things,mirrors being using to change the position of the laser beam used in thescan. To overcome these problems, an alternative calibration methodologyis needed and disclosed hereinafter.

I. Antipodal Calibration Rig

FIG. 1A illustrates an example of an antipodal calibration rig 100. Thisexample contains an antipodal telescope pair, 110 and 115, as well asother telescopes. The antipodal calibration rig 100 can be used forangular calibrations (as described in section III below), tiltcalibrations (as described in section IV below), and/or rangecalibrations (as described in section V below). In some embodiments, theantipodal calibration rig 100 includes a base 105 for a scanner 107within the calibration rig 100. The base 105 can include a four axisscanner manipulator 108. FIG. 1B illustrates the four axis scannermanipulator 108 of FIG. 1A. The four axis scanner manipulator 108 allowsfor small tilt movements of the scanner 107 about two axis, otherwiseknown as a tilt table, and a rotation about one axis, typically thestanding axis of the scanner 107. In addition, the manipulator 108allows a gross translation of the scanner 107 in order to remove theunit from between the antipodal telescopes. Alternatively, the base 105can include only tilt table (not shown), which has a top that can tiltin one or more directions, or any other device that allows propermovement of the scanner, including displacement and rotation.

In some embodiments, the calibration rig 100 includes one or moretelescopes 110, 115, 120 and 123. A telescope as used herein includes atarget behind a lens designed for the collection or focus ofelectromagnetic radiation. For example, the calibrations rig 100 caninclude a first telescope 110 and a second telescope 115. In someembodiments, the axis of the first telescope 110 and the axis of thesecond telescope 115 can be aligned antipodal to one another. Inmathematics, the antipodal point of a point on the surface of a sphereis the point which is diametrically opposite the original point—sosituated that a line drawn from the one to the other passes through thecentre of the sphere and forms a true diameter. Therefore, telescopesaligned antipodal to one another are telescopes that face each other andhave axes that are substantially parallel to one another. Aligningtelescopes in an antipodal pair may eliminate a degree of uncertainty,because the telescopes are in an antipodal pair, their orientations withrespect to one another are known. In other embodiments, the axis of thefirst telescope 110 and the axis of the second telescope 115 can beperpendicular to one another. In further embodiments, the axis of thefirst telescope 110 and the axis of the second telescope 115 can be atsome other angle relative to one another.

In other embodiments, the antipodal calibration rig 100 can include morethan two telescopes. For example, the antipodal calibration rig 100 caninclude a third telescope 120 and a fourth telescope 123. The axis ofthe third telescope 120 can be perpendicular to the axis of the firsttelescope 110. Additionally, the third telescope 120 can be antipodal tothe fourth telescope 123. Therefore, the calibration rig 100 can includefour telescopes aligned in 90 degree intervals around a circle.Antipodal alignment of one or more pair of telescopes may eliminate adegree of uncertainty (i.e. an unknown calibration parameter) becausethe alignment of one telescope relative to the other is known (asdescribed in section II below). Although example configurations aregiven, one of skill in the art will appreciate that the telescopes 110,115, 120 and 123 can be aligned in any combination to best calibrate thescanner 107.

In some embodiments, the antipodal calibration rig 100 includes targets125 that are not within a telescope. Targets 125 can be used much thesame way as telescopes. However, telescopes have the advantage overtargets 125 that telescopes appear to be much farther away. Theincreased “range” provided by the telescopes allows more precisecalibration. In some embodiments, the antipodal calibration rig 100includes range calibration elements 130.

In some embodiments, the telescopes 110, 115, 120 and 123 of theantipodal calibration rig 100 can include alignment lasers. Thealignment lasers can be used to indicate the axis of the telescopes 110,115, 120 and 123. This information may be used to align the telescope orother telescopes antipodal to one another (as described below in sectionII). The beam of the alignment lasers may be round or may be a reticleprojection. A reticle or crosshair is a shape superimposed on an imagethat is used for precise alignment of a device. Crosshairs are mostcommonly represented as intersecting lines in a “+” shape, though manyvariations exist, including dots, posts, circles, scales, chevrons, or acombination of these. A reticle projection may allow for more precisealignment of the telescopes 110, 115, 120 and 123.

Additionally, the targets in the telescopes 110, 115, 120 and 123 mayinclude autocollimators. An autocollimator is an optical instrument fornon-contact measurement of angles. Some autocollimators work byprojecting an image onto a target mirror, and measuring the deflectionof the returned image against a scale, either visually or by means of anelectronic detector. Therefore, the autocollimators can be used todetect the location of an incoming laser beam.

In some embodiments, the antipodal calibration rig 100 can be part of anantipodal calibration system (not shown). An antipodal calibrationsystem includes an antipodal calibration rig 100 and an environmentalchamber (not shown). The environmental chamber includes temperaturecontrols and is of sufficient size to surround the antipodal calibrationrig 100 (i.e. the antipodal calibration rig 100 is placed within theenvironmental chamber). This allows for calibrating three dimensionalscanning systems at multiple temperatures. Alternately the telescopes110, 115, 120 and 123 can be placed outside the environmental chamberand the scanner 107 placed inside the chamber. In such an embodiment,high quality windows allow the telescopes 110, 115, 120 and 123 to viewthe scanner inside the chamber.

II. Antipodal Alignment

FIG. 2 is a flow diagram illustrating an example of a method (200) foraligning a first telescope and a second telescope in an antipodal pair(e.g. in an antipodal calibration rig as described in section I above).Telescopes aligned antipodal to one another are telescopes that faceeach other and have axes that are substantially parallel to one another.Aligning telescopes in an antipodal pair may eliminate a degree ofuncertainty. Because the telescopes are in an antipodal pair, theirorientations with respect to one another are known, thus eliminating adegree of uncertainty.

The method (200) includes comparing, at the first telescope, theposition of the beam of the first telescope and the beam of the secondtelescope (205). The positions of the beams of the first telescope andthe second telescope can be compared in any appropriate manner. FIG. 3illustrates an example of comparing the position of alignment lasersusing a beam splitter. A beam splitter is an optical device that splitsa beam of electromagnetic (EM) radiation into two parts. The firsttelescope 300 includes a first alignment laser 305. The first alignmentlaser 305 can be used to indicate the axis of the first telescope 300.The beam of the first alignment laser 305 may be round or may be areticle projection.

The first alignment laser 305 is directed out of the first telescope300. For example, a beam splitting cube 310 can be used to direct thebeam of the first alignment laser 305 out of the first telescope. A beamsplitting cube 310 can be made from two triangular glass prisms whichare glued together at their base using, for example, Canada balsam. Thethickness of the resin layer is adjusted such that (for a certainwavelength) portion of the EM radiation incident through one “port”(i.e. face of the cube) is reflected and the other portion istransmitted. The first beam splitting cube 310 directs the beam of thefirst alignment laser 305 out of the first telescope 300.

After the beam of the first alignment laser 305 exits the firsttelescope 300 the beam encounters a third beam splitter 315. The thirdbeam splitter 315 can be a half-silvered mirror. A half-silvered mirrorcan include a plate of glass with a thin coating of aluminum (usuallydeposited from aluminum vapor) with the thickness of the aluminumcoating such that a first portion of the incident light is transmittedand a second portion is reflected.

Similarly, a second alignment laser 320 on the second telescope 325 issplit at a second beam splitting cube 330 and directed out of the secondtelescope 325. The beam of the second alignment laser 320 encounters thethird beam splitter 315, with the first portion of the light transmittedand the second portion of the light reflected.

The second portion of the first beam (which is reflected at the thirdbeam splitter 315) and the first portion of the second beam (which istransmitted through the third beam splitter 315) continue to the firsttelescope 300 where the second portion of the first beam and the firstportion of the second beam encounter the first beam splitting cube 310.A portion of the beams pass through the first beam splitting cube 310where the second portion of the first beam and the first portion of thesecond beam are incident on a first target 335 within the firsttelescope 300. The first target 335 can include an autocollimator, aposition sensitive diode, a focal plane array or any other device fordetecting the position of the first beam and the second beam. Anautocollimator is an optical instrument for non-contact measurement ofangles. A position sensitive diode (PSD—a.k.a. position sensitive deviceor position sensitive detector) is an optical position sensor that canmeasure the position of a light spot in one or two-dimensions on asensor surface. A focal-plane array (FPA—a.k.a. staring array,staring-plane array, or focal-plane, camera) is an image sensing deviceconsisting of an array (typically rectangular) of light-sensing pixelsat the focal plane of a lens. One of skill in the art will recognizethat any device that can adequately detect the positions of the firstbeam and the second beam can be used as the first target 335. Theposition of the first beam and the second beam can be compared at thefirst telescope 300 simultaneously in the embodiment of FIG. 3.

FIG. 4 illustrates an alternative embodiment for comparing the positionof alignment lasers using corner cubes. A pair of corner cubes 400A and400B is used to reflect the first beam back to the first telescope 405and the second beam back to the second telescope 410. A corner cube(a.k.a. corner reflector) is a retroreflector consisting of threemutually perpendicular, intersecting flat surfaces, which reflectselectromagnetic (EM) waves back towards the source. A retroreflector(sometimes called a retroreflector) is a device or surface that reflectsEM waves back to their source with a minimum scattering. Anelectromagnetic wave front is reflected back along a vector that isparallel to but opposite in direction from the wave's source. Therefore,the first corner cube 400A reflects the first beam back to the firsttelescope 405. The position of the first beam reaches a first target inthe first telescope 405 where the position of the first beam isdetected.

The pair of corner cubes 400A and 400B can then be moved into a secondposition (e.g. rotated 90 degrees) where the pair of corner cubes 400Aand 400B do not reflect the alignment laser beams. In some embodiments,the pair of corner cubes 400A and 400B can be located on a rotating arm415 to facilitate their movement. The beam of the second alignment laserthen reaches the first telescope 405 where the position of the beam ofthe second alignment laser can be detected and the position of the beamof the first alignment laser and the position of the beam of the secondalignment laser can be compared at the first telescope 405. The positionof the first beam and the second beam can be compared at the firsttelescope 405 sequentially in the embodiment of FIG. 4.

Returning again to FIG. 2, the method (200) further includes comparing,at the second telescope, the position of the beam of the first telescopeand the beam of the second telescope (210). In the embodiment of FIG. 3,the first portion of the first beam (which is transmitted through thethird beam splitter 315) and the second portion of the second beam(which is reflected at the third beam splitter 315) continue to thesecond telescope 325 where the first portion of the first beam and thesecond portion of the second beam encounter the second beam splittingcube 330. A portion of the beams pass through the second beam splittingcube 330 where the first portion of the first beam and the secondportion of the second beam are incident on a second target 340 withinthe second telescope 330. The positions of the beams can be compared atthe second target 340 in the same manner as the comparison at the firsttarget or in a different manner. The positions of the first beam and thesecond beam can be compared at the second telescope 340 simultaneouslyin the embodiment of FIG. 3.

One of skill in the art will recognize that the third beam splitter 315in the embodiment of FIG. 3 need not be positioned directly between thefirst telescope 300 and the second telescope 325, but can be positionedanywhere that allows adequate reflection of a portion of each beam tothe originating telescope and passes the remaining portion to the othertelescope. In some embodiments, the third beam splitter 315 can bepositioned so that a scanner (not shown) can be placed along the path ofthe beams, about midway between the first telescope 300 and the secondtelescope 325, for calibration. Additionally, the alignment lasers 305and 320 may be of a different wavelength than the scanner, whichindicates the beam splitter may be remain in place during angularcalibration.

In the embodiment of FIG. 4, the second corner cube 400B reflects thesecond beam back to the second telescope 410. The second beam reaches asecond target in the second telescope 410 where its position isdetected. The pair of corner cubes 400A and 400B can then be moved intoa second position (e.g. rotated 90 degrees) where the pair of cornercubes 400A and 400B do not reflect the alignment laser beams. The beamof the first alignment laser then reaches the second telescope 410 wherethe position of the beam of the first alignment laser can be detectedand the position of the beam of the first alignment laser and theposition of the beam of the second alignment laser can be compared atthe second telescope 410. The position of the first beam and the secondbeam can be compared at the second telescope 410 sequentially in theembodiment of FIG. 4.

One of skill in the art will recognize that the pair of corner cubes400A and 400B need not be positioned directly between the firsttelescope and the second telescope, but can be positioned anywhere thatthe corner cubes 400A and 400B can adequately reflect a portion of eachbeam to the originating telescope and pass the remaining portion to theother telescope. In some embodiments, the pair of corner cubes 400A and400B can be closer to one telescope so that a scanner can be placedalong the path of the beams, about midway between the first telescope405 and the second telescope 410, for calibrations. In otherembodiments, there may be a gap between the corner cubes 400A and 400Bto allow a scanner to be placed between the corner cubes 400A and 400B,about midway between the first telescope 405 and the second telescope410, for calibrations.

Referring again to FIG. 2, the method (200) further includes adjustingthe first telescope and the second telescope until the beams areparallel (215). The adjustment can be accomplished by moving thetelescopes or by aligning the telescopes in some other way. For example,mirrors within the telescope can be moved to adjust the first telescopeand the second telescope. The beams can be further adjusted until thebeams are collinear (i.e. the first telescope and the second telescopeshare a common axis).

The step of adjusting the first and second telescopes so that the beamsare collinear can be eliminated if theses telescopes are calibrated asautocollimators and the relative orientation of the telescopes areknown. Given the position of the alignment laser on the PSD or FPAinside the telescope, the angular direction of the laser beam in thecoordinate frame of the telescope can be known in the telescopecoordinate frame. Hence with either the corner cube reflectors shown inFIG. 4 or the beam splitter shown in FIG. 3, one can measure the angularposition of both alignment laser beams in both telescope coordinateframes. The relative orientation of the two telescopes can then befound. This is equivalent to having the telescopes collinear, that is,properly aligned.

Knowing the relative alignment of the first telescope and the secondtelescope in a proper antipodal pair can be critical in properlycalibrating a scanner. FIG. 5A illustrates a simulation 500 of the errorin calibration parameters due to measurement noise. FIG. 5B illustratesa simulation 550 of the error in calibration parameters due tomisalignment of an antipodal pair of telescopes used in calibrating thescanner. The error in calibration parameters due to noise is roughlylinear with a slope approximately equal to the square root of 2(approximately 1.4). The error in calibration parameters due toantipodal alignment is roughly linear with a slope approximately equalto the square root of eight (approximately 2.8). Therefore, misalignmentor mis-estimation of the relative alignment of the antipodal pair cancause appreciable error in the calibration parameters. Alternatively,proper alignment of the antipodal pair can lead to a high degree ofaccuracy in the calibration parameters of a scanner, leading to moreaccurate measurements by the scanner.

III. Angular Calibration

Angular calibration is a method which estimates the angular parametersof a scanner. The angular calibration parameters allow a user to computethe direction of scanner laser beam using the scanner internalmeasurements such as the encoder angles. Using the direction of thelaser beam together with the properly adjusted range, a coordinate ormeasurement in either Cartesian or spherical coordinates may bereturned. The spherical coordinate system is a coordinate system forrepresenting geometric figures in three dimensions using threecoordinates: (1) the radial distance of a point from a fixed origin, (2)the zenith (or elevation) angle from the positive z-axis to the point,and (3) the azimuth angle from the positive x-axis to the orthogonalprojection of the point in the x-y plane. However, regardless of thecoordinate system used, accurate angular measurements are important forthe accuracy of the scanner. While the scanner may be configured toemulate spherical or other coordinate systems, the internal measurementsof the scanner alone such as encoder angles and ranges must first betransformed using angular and range calibration parameters in order tocreate measurements independent of the scanner.

FIG. 6 is a flow diagram illustrating an example of a method forperforming an angular calibration of a three dimensional scanning system(600). The three dimensional scanning system may include a Light ImagingDetector and Ranging (LIDAR) scanner or any other type of threedimensional scanning system.

The method (600) includes locating the scanner within an antipodalcalibration rig (605) (e.g. an antipodal calibration rig as described insection I above). In some embodiments, the antipodal calibration rigincludes a first telescope and a second telescope. The first telescopeand second telescope may be either aligned antipodally or of knownrelative orientation (e.g. using the method described in section IIabove). The scanner is located on the axis of the first telescope andthe axis of the second telescope. By aligning the first telescope andthe second telescope antipodally, a degree of uncertainty may beeliminated. The antipodal telescopes have either parallel axes,therefore it is known that the two axes are 180 degrees apart, or have aknown relative alignment, with two axis apart by a known amount. Thisknown quantity eliminates one degree of uncertainty, or one variable, inthe calibration. In other embodiments, the antipodal calibration rig mayinclude more than two telescopes and one or more targets in addition tothe first telescope and the second telescope.

The first telescope and/or the second telescope can include a target.The target can include an autocollimator, a position sensitive diode, afocal plane array or any other device for detecting the position of thescanner beam. An autocollimator is an optical instrument for non-contactmeasurement of angles. A position sensitive diode is an optical positionsensor that can measure a position of a light spot in one or twodimensions on a sensor surface. A focal-plane array is an image sensingdevice consisting of an array (typically rectangular) of light-sensingpixels at the focal plane of a lens. One of skill in the art willrecognize that any device that can adequately detect the positions ofthe scanner beam can be used as a target.

The method (600) also includes measuring the angular location of thelaser beam in the coordinate frame of the first telescope (610) bypointing the scanner laser beam into the telescope and reading both theposition on the telescope target and the internal scanner angles Hencethe direction of the scanner laser beam is known in the coordinate frameof the telescope, and this direction is associated with a set of scannerangular measurements. In some embodiments, the measurement can be takenat a point on the telescope target which corresponds exactly to thelocation of one or both telescope alignment laser beams. In otherembodiments, the calibration of the telescope and target is used tomeasure the relative location of the scanner laser beam to the alignmentbeams. In some embodiments, measuring the angular location of the laserbeam of the scanner with respect to the first telescope (610) includesmeasuring the angular location using a two face measurement. A two facemeasurement includes observing the telescope, rotating the scanner aboutthe base (rotating around the z-axis, or the zero of the zenith axis)180 degrees, and repeating the observation of the same telescope. Arotation about the zenith axis of 180 degrees should produce asubsequent measurement of the zenith angle approximately equal to theinitial measurement of the zenith angle. The angular direction of thelaser beam for the second face measurement might not correspond to thesame angular direction of the first face measurement, provided thetelescope and target are calibrated and hence the direction of the laserbeam is known in the telescope coordinate frame.

The method (600) further includes measuring the angular location of thescanner laser beam in the coordinate frame of the second telescope (615)in the same manner as described for the first telescope. In each case,the direction of the laser beam in the coordinate frame of thetelescopes is measured together with the matching set of internalscanner angles, and this is done in both faces. The angular location ofthe second telescope can be described with two angles; the zenith anglefrom the positive z-axis to the telescope (specifically, the focal pointof the telescope), and the azimuth angle from the positive x-axis to theorthogonal projection of the telescope (specifically, the focal point ofthe telescope) in the x-y plane. However the angular locations of thefirst and second telescopes are not known. Because the telescopes areplaced in an antipodal arrangement and they contain alignment lasers,their relative alignment is known and this is enough to solve thecalibration and as a result the angular locations of the telescopes.

In some embodiments, measuring the angular location of the scanner laserbeam in the coordinate frame of the second telescope includes measuringthe angular location using a two face measurement. A rotation about thezenith axis of 180 degrees should produce a subsequent measurement ofthe zenith angle approximately equal to the initial measurement of thezenith angle. The angular direction of the laser beam for the secondface measurement might not correspond to the same angular direction ofthe first face measurement, provided the telescope and target arecalibrated and hence the direction of the laser beam is known in thetelescope coordinate frame.

The method (600) further includes estimating a set of angularcalibration parameters from the measurements (620). After themeasurements are completed, the angular location of the laser beam isknown in the coordinate frame of the telescopes for at least fourdifferent scanner laser beam directions, that is, both front and backface measurement on both telescopes. These observations can then be usedto compute the scanner angular calibration parameters using standardnonlinear programming techniques, such as a modified bundle adjustment.The angular parameters may include azimuth offset, elevation offset,elevation alignment, mirror alignment, and laser alignment about y and zaxes. Azimuth offset (or the zero of the azimuth angle) may be anexterior parameter and may be chosen by definition rather than by someintrinsic configuration of the scanner itself. Elevation offset (thezero of the zenith angle) is the zero angle of the scanner perpendicularto the Azimuth axis. Elevation offset is relative to the azimuth(“standing”) axis. Elevation alignment is the angle between theelevation axis and the azimuth axis. Ideally, elevation alignment wouldbe exactly 90 degrees (perpendicular) but may not actually be 90degrees, so the real elevation alignment must be known. Mirror Alignmentis the alignment of the mirror of the scanner with respect to theelevation axis. Ideally mirror alignment would be 45 degrees, but willnot actually be 45 degrees, so the real mirror alignment must be known.Laser Alignment about the y and z directions is the directionalalignment of the laser beam relative to the elevation axis before thelaser intersects the mirror. Ideally the laser would align with thex-axis (azimuth axis) but the deviation must be known.

In some embodiments, the angular parameters may be different than thoselisted above. Different sets of parameters may describe the samevariations and in such a case a method to compute one set of parametersfrom the other would exist. Two parameterizations linked by such amethod are considered equivalent. Other sets of parameterizations mightinclude different variations in scanner behavior. In other embodiments,there are more or less parameters depending on manufacturing defects inthe scanner and on the physical construction of the scanner. The methoddisclosed does not depend on the particular representation orparameterization of the scanner but rather on the use of telescopeswhich are placed in an antipodal manner and hence can observe theirrelative orientation.

IV. Tilt Calibration

Tilt calibration is a process which estimates the tilt calibrationparameters of a tilt sensor mounted in a scanner. A tilt sensor measuresthe scanner's relative tilt around horizontal axes, or the pitch androll of the scanner with respect to gravity. Knowing the direction ofgravity with respect to the direction of the laser beam facilitateslinking measurements taken at different times or locations together.Tilt calibration is critical to correlating measurements in thereference frame of the scanner to positions of measured points.

FIG. 7 is a flow diagram illustrating an example of a method forperforming a tilt calibration of a three dimensional scanning system(700). The three dimensional scanning system may include a LIDAR scanneror any other type of three dimensional measuring system.

The method (700) includes locating the scanner on a tilt table within ancalibration rig (705) (e.g. a telescope based angular calibration rig asdescribed in section I above). A tilt table can tilt the scanner in oneor more directions. The tilt table can, for example, be embodied by thefour axis scanner manipulator. The antipodal calibration rig includesone or more telescopes mounted on the antipodal calibration rig. Two ormore telescopes may be used as a reference to measure the tilt of thescanner.

The method (700) may also include performing an angular calibration ofthe scanner (710). Angular calibration can be performed according to themethod described above in section III or can be performed in some othermanner. Angular calibration ensures that the scanner is accuratelymeasuring angles. However, regardless of the coordinate system used,accurate angular measurements are important for the accuracy of thescanner. Additionally, accurate tilt measurements require accurateangular measurements.

The method (700) further includes solving for the tilt index of thescanner (715). The tilt index is the offset of the tilt sensor. A tiltsensor may be mounted in some unknown way to a system. Therefore, a tiltmeasurement has no physical reference by itself. In some embodiments,the system is rotated around the azimuth axis and tilt measurements aretaken along the way. The tilt measurement will describe locally acircle. The center of the circle is this index. If the scanner is tilteduntil the tilt sensor read the index value, then rotating the scannerabout the azimuth axis will not change the output of the tilt sensor.The location of the index can also be found by what is known as a twoface tilt correction. The process consists of first measuring the outputof the tilt sensor at one fixed location, then rotating the scannerabout its azimuth axis by 180 degrees and measuring the output of thetilt location at the second location. The average output of the tiltsensor is then the index value.

Once the index of the tilt sensor is measured, the position of at leasttwo telescopes is measured by pointing the laser beam into saidtelescope and measuring the laser beam location. Because the angularcalibration of the scanner is known, the direction of the laser beam isknown, and hence the location of the telescope in the coordinate frameof the scanner is determined. The two telescopes chosen should not beanti-podal or nearly so.

The method (700) also includes moving the tilt table to a next tiltposition (720). In some embodiments, the next tilt position may bearbitrary. In other embodiments, the next tilt position can becalculated, or approximately calculated before moving the tilt table tothe next tilt position. At the next tilt position an actual output ofthe tilt sensor is obtained (725). The tilt sensor of the scanner willindicate some tilt, even in the absence of calibration. This is theactual output of the tilt sensor. The position of two or more telescopesin relation to the next tilt position is also measured (730). Using themeasurement of the position of the two or more telescopes, the actualchange in orientation of the scanner can be computed. The actual changein orientation of the scanner can then be compared, after computing theexpected output of the tilt sensor, to the measured output of the tiltsensor.

The method (700) also includes repeating for a total of three or moretilt positions (740), moving the tilt table to a next tilt position(720), obtaining the actual output of the tilt sensor (725), measuringthe position of two or more telescopes (730) and computing the expectedoutput using the measured positions (735). In some embodiments,repeating for a total of three or more tilt positions (740) includesrepeating for a total of ten or more tilt positions. Repeating for atotal of ten or more tilt positions may allow a set of estimated errorsin the tilt parameters to be computed.

The method (700) further includes computing an estimated tilt sensormodel by comparing the expected output of the tilt sensor to the actualoutput of the tilt sensor (745). In some embodiments, the tilt sensormodel can include tilt in the calibration rig, scale factors, crossterms and orientation about gravity. Tilt in the calibration rig is thepitch and roll of the sensor. Scale factors correct between the measuredtilt and the output of the tilt sensor. For example, when the actualtilt is 10″ (10 arc seconds), the measured tilt may be 9.5″. Cross termsare the mix the output of different tilt directions (i.e. it isdifficult or impossible to have pitch, without the sensor alsoindicating roll, and vice versa). Orientation about gravity allowsconversion of pitch and roll of the tilt sensor to pitch and roll in thescanner coordinate frame.

In some embodiments, the tilt sensor model can be solved using leastsquares. The <method of least squares (or ordinary least squares OLS) isused to solve over determined systems (systems with more equations thanunknowns). Least squares is a method of fitting data. The best fit inthe least-squares sense is that instance of the model for which the sumof squared residuals has its least value, a residual being thedifference between an observed value and the value given by the model.One of skill in the art will recognize that there are multiple methodsby which a model for the tilt sensor may be estimated, least squaresbeing only one, and that any preferred method can be used.

Pitch is rotation around one horizontal axis. For example, in flightdynamics, pitch is rotation around the lateral or transverse axis—anaxis running from the pilot's left to right in piloted aircraft, andparallel to the wings of a winged aircraft; thus the nose pitches up andthe tail down, or vice-versa. Roll is rotation around the otherhorizontal axis. For example, in flight dynamics, roll is rotationaround the longitudinal axis—an axis drawn through the body of theaircraft from tail to nose in the normal direction of flight, or thedirection the pilot faces. Yaw is rotation about the vertical axis—anaxis drawn from top to bottom, and perpendicular to the other two axes.

A minute of arc, arcminute, or MOA is a unit of angular measurement,equal to one sixtieth ( 1/60) of one degree. Since one degree is definedas one three hundred sixtieth ( 1/360) of a circle, 1 MOA is 1/21600 ofthe amount of arc in a closed circle. The standard symbol for markingthe arcminute is the prime (′). The subdivision of the minute of arc isthe second of arc, or arcsecond. There are 60 arcseconds in anarcminute. Therefore, the arcsecond is 1/1296000 of a circle, or(π/648000) radians, which is approximately 1/206265 radian. The symbolfor the arcsecond is the double prime (″).

In some embodiments, a scanner with angular and tilt calibrationsperformed using an antipodal calibration rig can be a 1″ scanner(accurate to within 1 arcsecond). This translates to an accuracy of 1 mmat a distance of 200 meters. Typical scanners have an accuracy of12-30″, so the improved calibration offered by using an antipodalcalibration rig according to the teachings disclosed herein issubstantial. This level of accuracy approaches the best accuracyprovided by total stations.

V. Range Calibration

Range calibration ensures that the scanner is accurately measuringdistance to a scanned point. Three dimensional scanning systems mayreturn the coordinates of a point in spherical coordinates. Thespherical coordinate system is a coordinate system for representinggeometric figures in three dimensions using three coordinates: theradial distance of a point from a fixed origin, the zenith angle fromthe positive z-axis to the point, and the azimuth angle from thepositive x-axis to the orthogonal projection of the point in the x-yplane. Because the point may be represented in spherical coordinates,accurate range measurements in a three dimensional scanning system arecrucial. However, regardless of the coordinate system used, accuraterange measurements are important for the accuracy of the scanner.

FIG. 8 is a flow diagram illustrating an example of a method forperforming a range calibration of a three dimensional scanning system(800). The three dimensional scanning system may include a LIDAR scanneror any other type of three dimensional scanning system.

The method (800) includes transmitting a beam from the scanner to arange calibration rig (805). In some embodiments, the beam istransmitted to a receiving telescope of the range calibration rig, andfocused onto a receiving fiber of the range calibration rig. FIG. 9Aillustrates an example of a range calibration rig 900. The rangecalibration rig 900 includes a receiving telescope 905 for receiving thebeam from the scanner 907. The receiving telescope 905 focuses the beamonto a receiving fiber 910. In other embodiments, the range calibrationrig 900 includes an open air network and the receiving telescope 905 maynot be needed.

Referring again to FIG. 8, the method (800) also includes splitting thebeam (810). In some embodiments, the beam is split using a beamsplitter. A beam splitter is an optical device that splits a beam of EMradiation into two parts. In other embodiments, the beam is split usinga fiber splitter. A fiber splitter is a device for splitting portions ofan optical signal transmitted in an optical fiber. The range calibrationrig 900 of FIG. 9A includes a fiber splitter 915.

The two parts of the signal need not be equal in power. In someembodiments, the first portion can have a higher portion of the opticalpower. For example, the first portion could contain 95% of the originalpower, with the second portion containing 5% of the power. In otherembodiments, the first portion could include 90%, 75%, 50%, or any otherpercentage suitable to perform the range calibration.

Referring again to FIG. 8, the method (800) further includes sending thefirst portion of the beam to a recirculating fiber loop and returningthe first portion to the beam splitter (815), fiber splitter or otherdevice for splitting the beam. In some embodiments, the recirculatingfiber loop may be a fiber optic cable of known length. The rangecalibration rig of FIG. 9A includes a recirculating fiber loop 920 ofknown length. The recirculating fiber 920 returns the optical signal tothe receiving fiber 910 using a fiber combiner 925. In otherembodiments, the recirculating fiber loop 910 may be replaced with anopen air network with an optical path of known length.

Referring again to FIG. 8, the method (800) also includes transmittingthe second portion of the beam back to the scanner (820). In someembodiments, the second portion can be transmitted using a transmittinglens. The range calibration rig of FIG. 9A includes a transmitting lens930 for returning the second portion to the scanner 907. In otherembodiments, for example in an open air network, the second portion canbe directed, using mirrors or other suitable components, to the scanner907. Because a second portion is split from the optical signal everytime the first portion passes through the splitter 915, pulses will betransmitted to the scanner 907 at regular intervals, with each pulsedecreasing exponentially in power. FIG. 9B illustrates the pulses 950A,950B, 950C and 950D transmitted from the range calibration rig 900 tothe scanner 907 showing the decrease in power.

Referring again to FIG. 8, the method (800) further includes measuringthe time between the pulses at the scanner (825). FIG. 9B illustratesthe time intervals being measured. The first time interval 955 indicatesthe time that the beam requires to travel through the range calibrationrig 900 and begin returning to the scanner 907. The pulses continue toarrive at the scanner 907 at regular intervals 960 thereafter, with theinterval 960 corresponding to the time the pulse takes to travel throughthe recirculating fiber 920. The first time interval 955 is notnecessarily, but may be, longer than the second interval 960.

Referring again to FIG. 8, the method (800) also includes calculatingthe range scale using the measured time between pulses (830). In someembodiments, the observed length of the recirculating fiber may becalculated by multiplying the speed of light in the fiber by the timebetween pulses. In other embodiments, the observed length of the opticalpath in the open air network may be calculated by multiplying the speedof light in the open air network by the time between pulses. The rangescale can then be calculated by comparing the known length of therecirculating fiber or open air network against the observed length.

The present invention may be embodied in other specific forms withoutdeparting from its spirit or essential characteristics. The describedembodiments are to be considered in all respects only as illustrativeand not restrictive. The scope of the invention is, therefore, indicatedby the appended claims rather than by the foregoing description. Allchanges which come within the meaning and range of equivalency of theclaims are to be embraced within their scope.

1. A method for angular calibration of a three dimensional opticalscanning system comprising: locating the three dimensional opticalscanning system within an antipodal calibration rig, wherein theantipodal calibration rig includes a first telescope mounted on theantipodal calibration rig and a second telescope mounted on theantipodal calibration rig, wherein the first telescope is alignedantipodal to the second telescope and the scanner is on an axis of thefirst telescope and an axis of the second telescope; measuring theangular location of the first telescope in two faces; measuring theangular location of the second telescope in two faces; and estimating aset of angular calibration parameters for the three dimensional opticalscanning system from the measurements.
 2. A method according to claim 1,wherein the three dimensional optical scanning system includes a LIDARscanner.
 3. A method according to claim 1, wherein the first telescopeis facing the second telescope and the first telescope and the secondtelescope have parallel axes.
 4. A method according to claim 3, whereinthe axis of the first telescope and the axis of the second telescope arecollinear.
 5. A method according to claim 1, wherein the first telescopeor second telescope include a target within the telescope for measuringthe angular location of the first telescope or the second telescope. 6.A method according to claim 5, wherein the target includes a positionsensitive diode for measuring the angular location of the firsttelescope or the second telescope.
 7. A method according to claim 5,wherein the target includes a focal plane array for measuring theangular location of the first telescope or the second telescope.
 8. Amethod according to claim 1, wherein the first telescope and secondtelescope include autocollimators for measuring the angular location ofthe first telescope or the second telescope.
 9. A method according toclaim 1, wherein the set of angular calibration parameters for the threedimensional optical scanning system include azimuth offset, elevationoffset, laser alignment in the y and z directions, elevation alignmentand mirror alignment.
 10. A method according to claim 1, furthercomprising: one or more additional telescopes mounted on the antipodalcalibration rig; measuring the angular location in two faces for the oneor more additional telescopes.
 11. A method according to claim 1,further comprising: one or more targets mounted on the antipodalcalibration rig; measuring the angular location in two faces for the oneor more targets.
 12. A three dimensional optical scanning systemcalibrated according to the method of claim
 1. 13. A method for aligninga first telescope and a second telescope of a three dimensional opticalscanner calibration system in an antipodal pair, wherein the telescopesinclude alignment lasers and a means for observing the first telescopeand second telescope is located between the first telescope and secondtelescope, the method comprising: comparing the position of a first beamof a first alignment laser of the first telescope against the positionof a second beam of a second alignment laser of the second telescope atthe first telescope; comparing the position of the first beam againstthe position of the second beam at the second telescope; and adjustingthe first telescope and the second telescope until the beams of thefirst alignment laser and second alignment laser are parallel.
 14. Amethod according to claim 13, wherein the first telescope and secondtelescope include at least one of: autocollimators for comparing theposition of the first beam against the position of the second beam;position sensitive diodes for comparing the position of the first beamagainst the second beam; and/or charge-coupled devices for comparing theposition of the first beam against the position of the second beam. 15.A method according to claim 13, further comprising adjusting the firsttelescope and the second telescope until the beams of both alignmentlasers are collinear.
 16. A method according to claim 13, wherein thealignment lasers include a reticle projection.
 17. A method according toclaim 13, wherein the means for observing includes a beam splitter andwherein: the comparison of the position of the first beam against theposition of the second beam at the first telescope is performedsimultaneously; and the comparison of the position of the first beamagainst the position of the second beam at the second telescope isperformed simultaneously.
 18. A method according to claim 17, wherein:the beam splitter is wavelength dependent; the alignment lasers are of adifferent wavelength than a scanner laser; and the antipodal alignmentof the first telescope and the second telescope occurs during acalibration of the scanner.
 19. A method according to claim 13, whereinthe means for observing includes a pair of corner cubes and wherein: thecomparison of the position of the first beam against the position of thesecond beam at the first telescope is performed sequentially; and thecomparison of the position of the first beam against the position of thesecond beam at the second telescope is performed sequentially.
 20. Amethod according to claim 19, wherein a pair of corner cubes are locatedin a first position along the first beam and the second beam or in asecond position not along the first beam and the second beam, the methodfurther comprising: at the first position: measuring the position of thefirst beam at the first telescope; and measuring the position of thesecond beam at the second telescope; and at the second position:measuring the position of the second beam at the first telescope; andmeasuring the position of the first beam at the second telescope.
 21. Amethod according to claim 20, wherein the pair of corner cubes ismounted on a rotating arm, the method further comprising rotating thepair of corner cubes between the first position and the second position.22. A method according to claim 13, wherein adjusting the telescopesincludes solving for an error and adjusting mathematically.
 23. A methodaccording to claim 13, further comprising locating the first telescopeand the second telescope on an antipodal calibration rig for performingangular and tilt calibrations of a three dimensional scanning system.24. A three dimensional optical scanning system calibrated using theantipodal telescopes of claim
 13. 25. An antipodal calibration rig forperforming angular or tilt calibrations of three dimensional opticalscanning systems comprising: a first telescope mounted on the rig; asecond telescope mounted on the rig; and a base for a scanner locatedwithin the antipodal calibration rig, wherein the base is configuredsuch that when the scanner is placed on the base the scanner is on anaxis of the first telescope and an axis of the second telescope.
 26. Anantipodal calibration rig according to claim 25, wherein the axis of thefirst telescope is either perpendicular or antipodal to the axis of thesecond telescope.
 27. An antipodal calibration rig according to claim25, further comprising: a third telescope, wherein an axis of the thirdtelescope is perpendicular to the axis of the first telescope; and afourth telescope, wherein the fourth telescope is antipodal to the thirdtelescope.
 28. An antipodal calibration rig according to claim 25,wherein one or more of the telescopes include alignment lasers andautocollimators.
 29. An antipodal calibration system comprising: anantipodal calibration rig according to claim 25; and an environmentalchamber for calibrating three dimensional scanning systems at multipletemperatures.